Gibrat’s Law indicates that the growth rate of a given firm is independent of its size. In the literature, both supporting and opposing opinions coexist. Scholars investigating firms exceeding the minimum scale tended to agree with Gibrat’s Law; for example, Hart and Prais (1956). In contrast, scholars investigating small firms tended to disagree with Gibrat’s Law; for example, Dunne and Hughes (1994). Recently, Lotti et al. (2003) analyzed the data of Italian manufacturing firms over the period from 1987 to 1993 and used quantile regression techniques to test whether Gibrat’s Law holds for new small firms in the early stage of their life cycle. Their main finding is that small firms have to rush in order to achieve a size large enough to enhance their likelihood of survival. Conversely, in subsequent years the patterns of growth rate of new smaller firms do to differ significantly from those of relatively larger entrants, and the Law cannot be rejected. This thesis applied the method of quantile regression and analyzed the data of DTI-Meeks-Whittington British firms over the period from 1955 to 1985. It aimed at using relatively older and larger firms’ data to compare with Lotti’s results and to compare the results from quantile regression with the results from the conventional method, OLS, which was used to investigate firms exceeding MES. In contrast to the results of Lotti et al. (2003), the results of this thesis indicate that Gibrat’s Law only holds at low-quantile and being rejected at other quantiles. In particular, the high-quantile in large firms tends to reject Gibrat’s Law. This finding is also different from the results of Hart and Prais (1956), which supported the Law while investigating firms exceeding MES.